Shift Parameter in the Backward Beam Method for Parabolic Problems for Preceding Times

摘要

Backward beam method (BBM) for numerical solution of parabolic problems for preceding times is considered. The BBM in Hilbert space is discussed. The BBM examined consists in finding a solution on a compact interval given the terminal value of the finite dimensional ordinary differential equation (ODE) system which is assumed to represent a continuous time, semidiscrete approximation to the parabolic partial differential equation under consideration (method of lines). The BBM is interpreted as a standard finite difference method for two point boundary value problems for second order ODE systems. This method is influenced by the choice of a spectral shift parameter. The expression for the optimal value by use of logarithmic convexity arguments for linear problems is explained via the numerical stability analysis of the forward and backward recurrence involved.